QuantBet Quantitative Analyst Challenge

A tennis match is played as a series of POINTS, contained within GAMES, which in turn are contained within SETS.

If a player reaches 4 or more points won in a game, and also has won 2 points more than their opponent, then they win that game.

If a player reaches 6 or more games won in a set, and also has won 2 games more than their opponent, then they win that set. If both players reach 6 games, then a TIE-BREAK is played to determine the winner of the set.

Suppose Djokovic plays a set of tennis against Murray under these rules, and his probablity of winning a point is 0.47. Assuming the probability of winning a point remains constant throughout, what would be the probability of Djokovic winning the set 6-4?